Question

12. Find the value of x.
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Answer 1

x = 16

Explanation:

since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.

∠ STR = ∠ SRT = 4x - 28

∠ STR and ∠ STU are a linear pair and sum to 180° , that is

9x + 4x - 28 = 180

13x - 28 = 180 ( add 28 to both sides )

13x = 208 ( divide both sides by 13 )

x = 16

Answer 2

x = 16

Explanation:

SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.

The angles opposite to equal sides are equal.

⇒ ∠STR = ∠R

∠STR = 4x - 28

Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair

∠STR + ∠STU = 180° {linear pair}

4x - 28 + 9x = 180

4x + 9x - 28 = 180 {Combine like terms}

13x- 28 = 180

Add 28 to both the sides

13x = 180 + 28

13x = 208

Divide both sides by 13

x = 208/13

`\sf \boxed{x = 16}`